## EDGE IRREGULAR REFLEXIVE LABELING FOR STAR, DOUBLE STAR AND CATERPILLAR GRAPHS

## EDGE IRREGULAR REFLEXIVE LABELING FOR STAR, DOUBLE STAR AND CATERPILLAR GRAPHS

*M. Ibrahim, S. Majeed, M. K. Siddiqui*

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## Abstract

A graph labeling is an algorithm that assignment the labels, traditionally represented by integers, to the edges or vertices, or both, of a network(graph) G. For- mally, given a graph G = (V;E), a vertex labeling is a function of V to a set of labels. A graph with such a function dened is called a vertex-labeled graph. Likewise, an edge labeling is a function of E to a set of labels. In this case, the graph is called an edge- labeled graph. We study an edge irregular re exive k-labeling for the star, double star and caterpillar graphs and determine the exact value of the re exive edge strength for these graphs.

## Keywords

edge irregular re exive labeling, re exive edge strength, star, double star, caterpillar